That code is either missing something or you managed to mess things up. Why invoke the backup twice? Check syntax, punctuation and correct order of commands given. (it's an exercise, try finding the fault yourself)

Thanks to both Dutch_Master and nelz for their help. Actually, you're right Dutch_Master for suggesting it as an exercise. I looked at the code over and over, compared it to other if elif else conditionals and came to the same conclusion that you and nelz stated. The then is in the wrong place.
The strange part is that this code was taken directly from the ShellScripting article on page 51 of LXF#126. Seems no one has actually tried the code out or no correction was ever published unless it was caught in a later issue of LXF. If it wasn't maybe someone should inform the publishers of a correction for this script.
Could you please answer one more question I have about this script? I'm not sure what you mean by code tags Dutch_Master, so if I do it wrong below please show me how to correct it.
What does this mean?

refer to? I assume it's some kind of path statement Also, how would I restore the files only and not the folder? For example, I used the script as an exercise to backup the Pictures folder in another folder called BackupFolder. How do I restore the Pictures folder w/o restoring the BackupFolder inside the Pictures folder (i.e when I run the restore.sh script I get the BackupFolder inside the Pictures folder which, in turn, stores the actual pictures.)

I can create the tarball. $1 is the Backup folder I created under the home folder. My scripts are in a Shellscripting folder I created also under the home folder. Here is the code I used to run the compress.sh script contained within the Shellscripting folder.

Actually I corrected an out of place then statement (This was taken from LXF#126) My question is, if I am in my Shellscripting folder and run the restore.sh script, how do I get it to see the backup.tar.gz archive in the parent directory of my Shellscripting folder so that line 2 in the script above will carry out lines 4 to 7? I can restore successfully if I specify the Backup folder as $1. Then lines 8 to 12 do the job, but how can I use the archived tarball to restore?

LXF126 is quite a while ago, so I can't remember exactly, but IMO it is the intention of the script to specify the required backup to restore. You may have made more then one backup over a period of time, so which one should the script use to restore?